The minimization of a TV-associated problem can be non-trivial due to the non-linearity and non-differentiability of the TV regularization term. In image processing, many efficient optimization algorithms have been developed for this task, including iteratively reweighed least squares [1]}, primal dual [2]}, split Bregman [3]}, and fast iterative shrinkage-thresholding algorithm (FISTA) [4]}, [5]}. Recently, alternating direction method of multipliers (ADMM) [6]}, [7]}, [8]}, [9]} has become increasingly popular. The elegance of ADMM lies in decomposition of the original minimization problem into several simple subproblems, each of which either has a closed-form solution or can be iteratively solved with efficient numerical methods. However, since ADMM-based methods have been implemented mainly for Cartesian grids using a forward-backward FDM [10]} and it is not straightforward to generalize them to solve the inverse problem on an unstructured domain. Moreover, the non-linearity of the data fitting term in Eq. (REF ) further complicates the DOT reconstruction problem, making the minimization process required to solve Eq. (REF ) difficult.
